Frbs which occur on particular dry kinds of soil, such as lime- **rf** one rocks, stiff clay, and so forth (Warming, 1909: 289).

If al, a2, ...a, n be the roots of f=o, (1, R2, -Ai the roots of 0=o, the condition that some root of 0 =o may qq cause f to vanish is clearly R s, 5 =f (01)f (N2) ï¿½ ï¿½;f (Nn) = 0; so that **Rf**,q5 is the resultant of f and and expressed as a function of the roots, it is of degree m in each root 13, and of degree n in each root a, and also a symmetric function alike of the roots a and of the roots 1 3; hence, expressed in terms of the coefficients, it is homogeneous and of degree n in the coefficients of f, and homogeneous and of degree m in the coefficients of 4..

**Rf** > a> b> o> a'> -Do; and then so that PT =c/Zir, and the curve AP is the tractrix; and the coefficient of contraction, or breadth of the jet breadth of the orifice - +i' A change of S2 and 0 into nS2 and nO will give the solution for two walls converging symmetrically to the orifice AA 1 at an angle zr/n.

30, 46 a 30), or the De Interpretatione, which he calls " the present theory " (**rf** j s 'Dv Oecopias, De Int.

When k2> 4u, the solution of (29) is, in real form, x = aie-_t/ri +aie)**rf**, (32)

Where ri, **rf** are the distances of mi, rni from their mass-centre G.

The frequency equation is therefore (o2g/a)(if2g/b) ~ (12) The roots of this quadratic in **rf** are easily seen to be real and positive.

A condition equivalent to the above, and necessarily connected with it, is, that at each pair of points of contact the inclinations of the curves to their radii-vectores shall be equal and contrary; or, denoting by r1, **rf** the radii-vectores at any given pair of points of contact, and s the length of the equal arcs measured from a certain fixed pair of points of contact dri/ds= drm/ds; (18)

In which ri is the greater radius, and **rf** the less.

Then v = ri (ri +ri)12 = (ri **rf**)2/2lrc. (34)

To express this symbolically, let Wi, W2 be the weights of the bodies; P the effort exerted between them; S the distance through which it acts; R1, **Rf** the resistances opposed to the effort overcome by Wi, ~AT2 respectively; E1, Ef the shares of the whole energy E exerted upon Wi, W2 respectively.

**Rf**. ?